The tight focusing properties of Laguerre-Gaussian-correlated Schell-model beams

Abstract

Based on the Richards–Wolf vectorial diffraction theory, the tight focusing properties, including the intensity distribution, the degree of polarization and the degree of coherence, of the Laguerre–Gaussian-correlated Schell-model (LGSM) beams through a high-numerical-aperture (NA) focusing system are investigated in detail. It is found that the LGSM beam exhibits some extraordinary focusing properties, which is quite different from that of the GSM beam, and the tight focusing properties are closely related to the initial spatial coherence δg and the mode order n. The LGSM beam can form an elliptical focal spot, a circular focal spot or a doughnut-shaped dark hollow beam at the focal plane by choosing a suitable value of the initial spatial coherence δg, and the central dark size of the dark hollow beam increases with the increase of the mode order n. In addition, the influences of the initial spatial coherence δg and the mode order n on the degree of polarization and the degree of coherence are also analysed in detail, respectively. Our results may find applications in optical trapping.